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In a small bowl combine flour, salt, pepper and parmesan cheese. Moisten chicken breasts with water and dredge them thoroughly in the flour mixture, until well coated. Shake off the excess.
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Heat the oil and 2 Tbsp of butter in a large skillet. Pan-fry the chicken pieces until golden brown on both sides, about 3 minutes per side.
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Work in batches, do not crowd skillet, add oil if needed. Remove the chicken from skillet and set aside. Drain most of the oil from the skillet, leaving a thin coating on the surface of the pan.
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Add the white wine or chicken stock, lemon juice, and capers to the pan. Use a spatula to dissolve (or “deglaze”) the brown bits from the bottom of the skillet. Let cook, stirring occasionally, until the sauce reduce by half.
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Whisk in the remaining 2 tablespoons of butter, until the butter is melted and incorporated. Add the parsley, remove from heat and set aside.
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Arrange the chicken over pasta or mashed potatoes on serving plates and drizzle the sauce over each portion. Garnish with fresh lemon slice and more fresh parsley, if desired.
